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# Of the 20 lightbulbs in a box, 2 are defective. An inspector

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Of the 20 lightbulbs in a box, 2 are defective. An inspector [#permalink]  20 Jan 2016, 08:44
Expert's post
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Question Stats:

70% (00:52) correct 30% (00:58) wrong based on 10 sessions
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?

Practice Questions
Question: 24
Page: 344
Difficulty: medium

[Reveal] Spoiler: OA
$$\frac{153}{190}$$

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Moderator
Joined: 18 Apr 2015
Posts: 4476
Followers: 67

Kudos [?]: 878 [0], given: 4107

Re: Of the 20 lightbulbs in a box, 2 are defective. An inspector [#permalink]  20 Jan 2016, 08:49
Expert's post
Solution

The question is a bit tricky.

If you have to choose the NON defective light bulbs, then you must choose among 18 good one.

So, you do have $$\frac{18}{20} * \frac{17}{19} =\frac{153}{190}$$

The correct answer is $$\frac{153}{190}$$
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GRE Instructor
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Re: Of the 20 lightbulbs in a box, 2 are defective. An inspector [#permalink]  23 Mar 2018, 13:02
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KUDOS
Expert's post
Carcass wrote:
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability
that neither of the lightbulbs selected will be defective?

Practice Questions
Question: 24
Page: 344
Difficulty: medium

[Reveal] Spoiler: OA
$$\frac{153}{190}$$

P(neither lightbulb is defective) = P(BOTH lightbulbs work)
= P(1st lightbulb works AND 2nd lightbulb works)
= P(1st lightbulb works) x P(2nd lightbulb works)
= 18/20 x 17/19
= 9/10 x 17/19 [since 18/20 = 9/10]
= 153/190

ASIDE: P(1st lightbulb works) = 18/20, because there are 20 lightbulbs and 18 of them work.
P(2nd lightbulb works) = 17/19 because, once we have selected a working bulb for the 1st selection, there are 19 lightbulbs remaining and 17 of them work.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: Of the 20 lightbulbs in a box, 2 are defective. An inspector   [#permalink] 23 Mar 2018, 13:02
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